This paper analyzes a supply chain, which consists of a manufacturer, a retailer and several suppliers in which the retailer orders jobs to the manufacturer and the suppliers provide the requiring parts. The manufacturer schedules and processes the orders and dispatches them to the retailer either individually or collectively in batches. The manufacturer incurs a penalty cost for each tardy job and a transportation cost for every delivered batch and therefore, searches for a schedule that yields minimum number of tardy jobs and batches. Moreover, the manufacturer tries to optimize its supplying cost through locating the suppliers that offer appropriate release times and costs for manufacturing parts. Since the release times of parts directly affect scheduling of orders, in this research, we develop an integrated mathematical model for the manufacturer that incorporates suppliers & apos; selection issue into the scheduling and batching decisions. Furthermore, we present a heuristic algorithm (greedy algorithm) and also a local search to quickly determine the optimal or near-optimal solutions. The computational analysis shows the importance of the integrated model and also the superiority and effectiveness of the heuristic algorithms.

This study investigates minimizing the number of weighted tardy jobs on a single machine when jobs are delivered to either customers or next station in various size batches. In real world, this issue may happen within a supply chain in which delivering goods to customers entails costs. Under such circumstances, keeping completed jobs to deliver in batches may result in reducing delivery costs; nevertheless, it may add to the tardy jobs, which in turn leads to higher costs. In literature review, minimizing the number of weighted tardy jobs is known as NP-Hard problem, so the present issue aiming at minimizing the costs of delivering, in addition to the aforementioned objective function, remains an NP-Hard problem. In this study, the issue is assessed where the customers are numerous, and a mathematical model is presented. We also present a meta-heuristic method based on simulated annealing (SA) and the performance of the SA is examined versus exact solutions.

This paper deals with a single-machine scheduling problem with maintenance activities. Our purpose is to provide a near optimal solution using metaheuristics approach. In this problem, there are n jobs and m machines (m?n), each job must be assigned to one and only one machine, where the processing time of job (j) is (p_j). Furthermore there are M_G groups where each group has a fix periodic interval T and for each group, the maximum number of jobs processed in the machines available time interval (T) is K, (M_G=m/K). For finding the near optimal solution, we consider optimizing total cost scheduling problem. This problem has two types of costs, group cost and gap cost. In this study, first, proposed problem is formulated in a mathematical model. Next, a heuristic genetic algorithm is used to obtain the proposed problem and on example is presented to verify the efficiency of the algorithm.